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I'm fairly new to chemistry, and I have a hard time understanding how chemical energy is stored in carbon (I'm aware that the question can be generalised to 'how is chemical energy stored', but I'm trying to understand it in the example of carbon). In the example in my book, carbon and oxygen react to form carbon dioxide, releasing energy in the form of warmth in the process.

My book says that the energy released in this process mainly comes from carbon, which is originally the solar energy stored by plants. I have to tried to look for explanations how that energy is stored (not how the process of photosynthesis works, but in what form or what is the meaning of the 'stored energy'), but I still can't really wrap my head around it. The best answer so far was What is the nature of chemical energy?

If I understand the answer there correctly, the bond potential energy of a carbon dioxide molecule is lower than the combined bond potential energy of a carbon atom and an oxygen molecule. Given that, there are still two things I don't understand:

  • Why is the bond potential energy in the carbon atom and/or oxygen molecule higher than that of a dioxide molecule? How can that explained? Is this directly related to the chemical traits of the elements carbon and oxygen and the compound carbon dioxide?
  • Why, or better said how is said bond potential energy converted to warmth in the process?

I'm aware that there might be concepts in physics here I don't know or understand to understand a possible answer, and I would be thankful for any pointers to what subjects I should be first reading to understand such an answer.

Edit: I would like to quote here something I came across on wikipedia. I'm not providing it as an answer nor claiming it is correct, just trying to illustrate how confusing it is to find a satisfying answer for this matter. This comes from https://en.wikipedia.org/wiki/Chemical_bond#Overview_of_main_types_of_chemical_bonds:

In the simplest view of a covalent bond, one or more electrons (often a pair of electrons) are drawn into the space between the two atomic nuclei. Energy is released by bond formation. This is not as a reduction in potential energy (sic), because the attraction of the two electrons to the two protons is offset by the electron-electron and proton-proton repulsions. Instead, the release of energy (and hence stability of the bond) arises from the reduction in kinetic energy due to the electrons being in a more spatially distributed (i.e. longer de Broglie wavelength) orbital compared with each electron being confined closer to its respective nucleus.

Italic and bold added by me. Note that wikipedia itself has a '[clarification needed]' tagging in the middle of that text, right after 'two protons', which I removed.

So if I understand that correctly and assuming that info is correct, any formation of a covalent bond would result in energy being released. But that still doesn't explain why my book is claiming the energy is particularly stored in carbon (and not in oxygen), and why it is released as warmth. In addition, the explanation on wikipedia would contradict what I referred to earlier, namely that the energy released comes from differences in bond potential energy.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Loong Jun 21 '17 at 11:17
  • $\begingroup$ "My book says that the energy released in this process mainly comes from carbon, which is originally the solar energy stored by plants." - what is this book, and is that a direct quote? $\endgroup$ – AakashM Jun 21 '17 at 11:50
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One of the most important issues in understanding bond energy in chemistry is the question: energy relative to what?

The formation of bonds from (mostly hypothetical) atomic elements releases energy (or they wouldn't be bonded.) Solid carbon (graphite or diamond) has less energy than a cloud of carbon atoms so it could be said graphite has less energy relative to a cloud of atomic carbon atoms. We would describe this energy as "bond energy". But this is the energy released by the hypothetical process of forming lists of C-C bonds from isolated carbon atoms.

But there is another subtle complication if we want to understand reactions. sometimes, when chemists write a reaction scheme they don't specify all the detail. So C +O2->CO2 doesn't actually mean atomic carbon atoms plus oxygen molecules give carbon dioxide. Most chemists would assume that the carbon starts in the state it is normally found as in laboratories: graphite (so not isolated atoms but a molecular solid containing lost of C-C bonds). This terminology seems to have confused some people. But chemists don't like to waste space in formulae redundantly specifying things most of their colleagues will already know. The default state of an ingredient in a reaction is assumed unless specified otherwise and this usually means the form the compound or element takes in a bottle on the lab shelf.

So how can we say that carbon stores energy? Well we have to ask the question, relative to what? In the case of the question the answer is relative to carbon dioxide gas. The point here is that the double bonds in CO2 are stronger than the combined bonds in oxygen gas and graphite (so they are lower energy) This means that the reaction between carbon and oxygen releases energy (it takes less energy to break all the O-O and C-C bonds than is released when new C=O bonds are formed. So elemental carbon "stores" energy relative to carbon dioxide.

The claim that carbon "stores" solar energy absorbed by plants is a little simplistic (mainly because plants don't store carbon but usually store more complicated molecules like sugars or poly-sugars like lignin or cellulose). Dead plants are converted to more carbon like compounds (oil is mostly hydrocarbons, but coal is mostly carbon) under some geological conditions. What plants actually do at the start of this process is to convert carbon dioxide into sugars using energy input from sunlight. They do this to store energy and to grow by converting the sugars into the structures of their leaves, stems and trunks.

We can reverse that process by burning the plants or their degradation produce like oil and coal in air to reproduce the carbon dioxide and release energy. In this highly simplified sense, carbon is a store of "solar" energy.

But the key to understanding what is meant is to understand the chemical reaction involved in the creation or burning of the carbon. Then you can understand what energy is stored and how it is stored.

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  • $\begingroup$ Just to make sure I understand you correctly: in my (rudimentary) understanding of a reaction, C + O2 -> CO2 means that one carbon atom and one oxygen molecule form together one carbon dioxide molecule. Maybe I don't understand the nature of a chemical reaction, but in that context, how can we speak of C-C bonds? $\endgroup$ – user46667 Jun 20 '17 at 9:00
  • $\begingroup$ Also, how should I understand the idea that a cloud of carbon atoms (maybe you meant a C-C molecule or otherwise carbon-based bond but I took it at face value?) has more energy relative to solid carbon? I might be understanding things a bit too literally here, but I'd like to know what exactly your usage of bond refers to in this context. Is this purely the forming of a molecule (as in covalent or otherwise any form of bond), or is it also simply "a lot of carbon atoms together at a given place" (= a piece of graphite). $\endgroup$ – user46667 Jun 20 '17 at 9:01
  • $\begingroup$ @user2311517 carbon, as normally found in nature as graphite, consists of a molecular solid with every carbon bonded to several other carbons. The reaction C + O2 is shorthand for solid carbon plus oxygen gas, so the reaction involves breaking lots of C-C bonds and O=O bonds resulting in CO2. You have to account for all the bonds broken and formed to know the energy difference. $\endgroup$ – matt_black Jun 20 '17 at 9:08
  • $\begingroup$ @user2311517 The "cloud" of carbon atoms is a hypothetical concept which we use to understand the relative bond energy of solid carbon: we don't find clouds of carbon atoms in nature: so C-C bonds exist in the natural state of carbon. $\endgroup$ – matt_black Jun 20 '17 at 9:10
  • $\begingroup$ In this case, it begs the question of why we are taught that pure O always comes in the form of a O2 molecule, while the form of C in the reaction can be pure, where in reality it is not? In other words, in this reaction, it is visible that we have an O2 bond which is broken, but it is not visible that we have a C bond with three other Cs which is also broken. That seems somewhat non-intuitive to me. $\endgroup$ – user46667 Jun 20 '17 at 9:19
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I realise that you are not interested in the mechanisms of photosynthesis or metabolism, however, as I am a biochemist, it will be easiest for me to explain this from a biochemical perspective. I will try to avoid talking about specific mechanisms. Regardless, I do believe that this may be able to help you understand this problem.

Bond potential energy is used to provide a means of "paying" for the cost of cellular processes that have no entropic gain. And as you have stated in your question, this all begins with photosynthesis.

Consider the carbon dioxide molecule. It consists of two $\ce{C=O}$ bonds - each of which contains a bond energy of $\ce{799kJ/mol}$. This inorganic form of carbon is the most stable of all carbons in a biological system. To break this bond, an input of energy greater than, or equal to $\ce{799kJ/mol}$ must be provided; in plants this energy is provided through photosynthesis.

So, to avoid going through how a plant builds energy-rich molecules, let us skip to the more interesting part: how is energy stored and utilized in carbon bonds created by photosynthesis?

As you don't seem to care much for mechanisms, I would like you to know that what I am about to say is a vast over-simplification. It will also be helpful to note that a $\ce{C-C}$ bond has an energy of $\ce{346kJ/mol}$, a $\ce{C-S}$ bond has an energy of $\ce{272kJ/mol}$, and a $\ce{S-H}$ bond has an energy of $\ce{363kJ/mol}$.

During metabolism, sugars will eventually be converted to a molecule called pyruvate. This pyruvate molecule will react with a thiol containing molecule called coenzyme A (CoA) to form acetyl-coenzyme A as follows:

enter image description here

The enthalpy of formation can be calculated as follows:

$$\pu{ΔH = ∑Bond energy reactant - ∑Bond energy of products}$$

For this reaction to occur, the following must happen:

  1. Break the $\ce{S-H}$ bond of the thiol of CoA
  2. Break the $\ce{C-C}$ bond of pyruvate
  3. Form a $\ce{C=O}$ bond of carbon dioxide
  4. Form a $\ce{C-S}$ bond of acetyl-CoA

This means that the enthalpy of formation:

$$\pu{ΔH = ( 346 + 363) - ( 799 + 272) = -362kJ/mol}$$

That is, this reaction releases 362kJ/mol worth of energy.

The best way to think about bond energies, is to consider that the "bond energy" is actually the amount of energy that is released (as heat or light) upon a bonds formation, or the amount of energy that must be provided (by heat or light) in order to break a bond.

When you have molecules, such as sugars, they are eventually broken down in such a way to form carbon dioxide - which we have seen to contain very high energy bonds. It is in the process of forming these $\ce{C=O}$ bonds, that the "stored" energy can be released.

I should also point out that the $\ce{O2}$ that enters a cell never actually directly participates in any reactions with carbon. $\ce{O2}$ will however be converted to two molecules of water, by reacting with an acid called NADH.

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Note that this is an edited answer. I have realised that there was initially a very severe error in my answer. Please re-read if you have not read this edited version.

In chemistry, we purely look at the energies in the process of bond breaking and bond formation when we look at energetics, as Zhe aptly pointed out in the comments. Thus, free atoms, such as a carbon atom, do not "store energy". As you have clarified in the comments, you wish to know, "in the context of the reaction $\ce{C + O2 -> CO2}$, where the released energy comes from, how it is stored in carbon, and how does it become warmth". In my response, I will tackle this 3-part question. Note that I will not consider nuclear chemistry and the interactions of subatomic particles, other than the particle chemists are most concerned about - the electron.

In chemistry, energy changes arise due to two key processes: the formation of a chemical bond and the breaking of a chemical bond, where the term "chemical bond" refers to any of the following: ionic bond, covalent bond, metallic bond and intermolecular force of attraction (although some may dispute this). Bond formation is an exothermic process while the breaking of a bond is endothermic. This is rather intuitive as energy is needed as input to overcome the force of attraction between atoms. The exothermic bond making process may not be so intuitive. However, you can simply think of it as an application of the conservation of energy: If bond breaking is established to absorb energy, the opposite would give off an equivalent amount of energy. Another intuitive explanation why this is so comes from a very important chemical principle: Chemical systems, in general, prefer to be in the more stable state (i.e. a lower-energy state). Thus, bond formation and exothermic reactions, in general, are favoured thermodynamically.

Part 1: In the combustion of elemental carbon, energy is given off by the exothermic formation of two strong carbon-oxygen double bonds (endothermic), while the oxygen-oxygen double bond is broken (exothermic). The overall enthalpy change of the reaction is exothermic as the sum of the bond energies of the bonds formed is greater than that of the bonds broken. Thus, energy is released from the reaction.

Part 2: No energy is stored in a carbon atom, in a chemical sense. Now, this is what has come upon me just this morning as I was reflecting on this question:

What stores energy in chemistry? It came upon me that the statement "bonds store energy" is very flawed. Thus, I am afraid I would have to say that Zhe is wrong in his comments. But neither is it correct to say "free atoms (or bonded atoms) store energy". As much as I would not like to use this analogy to answer this question for possible points of contention regarding the relevancy, I feel nevertheless that it is appropriate: Consider two simple bar magnets (i.e. magnetic dipoles) which are attracted to each other. What holds them together is a magnetic force. To pull them apart, we input energy into them as work in order to overcome the force. This system of magnetic dipoles is analagous to how atoms are bonded to each other, just that the force of attraction between the two atoms are much more complex and that the nature is electrostatic, not magnetic (of course, we now know that magnetism is very closely linked to electric charges in physics but that is not important for this discussion).

So going back to relevant examples, which would illustrate my next important point as to explain where energy changes comes from. Consider the chemical energy stored in food. We say that there is a chemical potential energy (at a very basic level of physics). But is that true? Does food and many fuels store energy? That may be correct from the point of view of the fuel undergoing reaction. Why do I say so? Remember: It is the process of bond formation and bond breaking that give off energy. Bonds themselves do not store energy. Only from reactions would we observe energy changes as energy is given off or taken in by the reactants to form products.

Let's go back to the combustion of elemental carbon. Using this perspective, neither carbon, nor carbon dioxide, nor oxygen store energy. The substances in the final and initial state do not store energy. In the process of bond formation and bond breaking, that energy is given off or taken in by the system.

Why do bonds not store energy? Well... bonds are merely electrostatic forces of attraction, in the most elementary sense. How can a force store energy?

Even if you don't believe the rest of my low-level explanation, please at least take away one thing: Bonds don't store energy.

Part 3: In chemistry, the energy is very often given off as heat in exothermic reactions. However, they can also be given off as light energy or sound energy.

Regarding your more difficult query about why energy is given off during bond formation, you can refer to my very brief explanation in Para 2. However, I fail to give you a detailed answer. Although I find no fault in Wikipedia's explanation based on the greater delocalisation of electrons upon bond formation, I do not believe that it is the main reason. Certainly, the strong attractive forces of the nucleus must be involved as well.

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Although this is not the actual reaction that living organisms utilize to produce $\ce{CO2}$, I think you have the reaction of formation of carbon dioxide in mind, which can indeed be explored to understand bond energy.

Let's have a box with pure carbon in some allotropic form, say graphite, immersed in an pure oxygen atmosphere. As time goes on - and it may indeed take a lot of time - the insistent collisions of oxygen molecules with the solid lattice will produce a chemical reaction. Think of throwing a bunch of keys randomly at a surface full of compatible locks. The keys aren't necessarily moving at the same speed or direction, so some of them will certainly bounce back from the surface - if they even get there, or they might not have sufficient speed to push itself into the lock. Nonetheless, some keys may have the exact appropriate motion to insert itself into a lock. But what does this keys unlocks? To proceed the analogy, the key unlocks that lock from the other ones, releasing it from that surface and bringing a key-lock pair onto the keys' flight path.

Now, remember from physics that when you presence a collision in which things stick, you probably have an inneslatic collision, where momentum is conserved but kinetic energy isn't. Some of that energy becomes heat. You seem to want to know how. But the real question should be why not?. Molecules move incessantly at random directions, exchanging momentum and energy chaotically. If you could canalize all molecular velocities to follow a main direction, you would have macroscopic motion and the energy to produce that phenomenon is called work. That's what's going on when you push or pull an object. When you stop pushing it, we observe that friction slows it down until it stops. Microscopically, the object molecules are colliding with the surface molecules over which it is sliding and also with the air molecules, both of which are somehow static in this reference frame, so they share momentum and energy until the object is also static and the molecules once again have no distinct preferential direction to follow.

The former kinetic energy of the object now belongs to the microscopic motion of molecules, which is randomly distributed. This is heat. The fact the same energy once visible at macroscopic motion is transferred in totality to the molecular realm is the first law of thermodynamics. The fact that energy in a certain way prefers to become heat is the second law of thermodynamics. Pull a string and release and it will oscillate for while with a decreasing amplitude, as its mechanical energy turns into thermal energy. This also happens with the key-lock lair. You could think of the mechanism as something like: key hits the lock, pushes itself in, transfers some kinetic energy and momentum with a normal direction with respect to the surface, the energy now belongs to the nearby surface elements, which then share this energy and distribute it along the other directions. If you're confused by this, don't worry. The underlying thermodynamics are mechanism-independent. So no matter how the phenomenon happens, we can conclude that for a sufficiently large amount of particles interacting, any energy that can become thermal energy certainly will within enough time.

The key-lock pair only fails to be a good analogy to the electronic energy of molecules. You might think of keys translating and rotating, just like molecules do and both certainly store energy within those degrees of freedom. But chemicals also present electrons, which move and interact, so they contain energy. Different atoms or molecules have different amount of electrons, with different levels of energy, which is related to all the quantum and electromagnetic interactions. This is hard stuff. We are better off thinking about chemical reactions simply as the movement of electrons - with the nuclei maintaining structure and "following" the electrons - towards more stable entities, with a lower energy, like the key inside the lock, and the energy is released as heat, not because there is some special mechanism to produce heat, but because heat is simplify unorganized energy, and it's the most likely product with septillions of molecules reacting altogether.

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